Irelia is easily one of my favorite champions due to her ability to destroy opponents late game, deal great burst damage, and be able to go head on against tanks late game. Now this is my first build so I'm hoping that I can help a few people out who like to use her. However I'm going to keep it brief with little facts you should know about her.

Pros
+Great End Game
+Chaser
+Crowd Control Has Minimal Effect
+Amazing Burst
+Good CC Use

Cons
+Squishy Early and Mid Game
+Very Dependent on Kills

Now farming can be difficult considering how squishy Irelia is early in the game and she isn't even ranged so it can be difficult around enemy champions. I like to get Bladesurge first off for its farming capabilities on mobs when playing the enemy team. You can finish a mob off back away and do it again with minimal to no damage. I don't suggest jungling until you at least have Sheen because you'll do little damage and have very little health to fight with. Later in the game always try to get the red buff because Irelia is deadly with it.

This sequence is incredibly useful because for the most part you'll be using a bladesurge/equilibrium combo right after popping hiten style for extra damage. Hiten style doesn't need to be leveled up excessively because the life steal properties are minimal in the beginning but help a lot end game and if it's activated helps even more. Also if you're low health and you have enemies pushing along with minions it can get you back to full health when used on a cluster of minions.